The state’s largest gay rights organization criticized sponsors of South Boston’s St. Patrick’s Day parade Wednesday, firing back with a sharply worded statement after being accused of dishonesty by parade organizers as relations between the two sides continued to fray.

MassEquality’s executive director, Kara S. Coredini, said she was “extremely disappointed” that parade organizers decided to “continue their long history of banning [gay] people from marching openly.”

The parade’s sponsor, the South Boston Allied War Veterans Council, had issued a press release earlier this week accusing MassEquality of lying on its application, “using a ploy to enter this parade under false pretenses,” saying it was not a legitimate veterans’ group.

The statement from the organizers marked an abrupt change in tone after days of discussions brokered by Mayor Martin J. Walsh. Both sides met in the mayor’s office Sunday night, and it seemed that a deal was within reach to end the two-decade prohibition against gays openly marching.

“We were under the impression that negotiations were positive and ongoing, and we were surprised by the abrupt and hostile tone of the parade organizers’ rejection,” Coredini said. “We regret that the parade organizers shut down conversation before an agreement could be finalized.”

Parade organizers could not be reached Wednesday for comment. Both sides have said that talks were over, but Walsh has continued to suggest otherwise. Walsh told reporters Wednesday that conversations between the sides continued Tuesday night, although he said he had not heard what took place.

“It’s been 22 years,” Walsh said. “It’s not going to be fixed overnight. We’re trying to solve this now.”

MassEquality’s parade application described a group of about 20 gay veterans and their families seeking to march alongside Walsh and state Senator Linda Dorcena Forry, a Haitian-American lawmaker from Dorchester who is scheduled to become the first person of color to host the St. Patrick’s Day breakfast political roast before the parade. Dorcena Forry has said she will boycott the parade if the gay community cannot march openly.

The gay veterans group proposed wearing MassEquality T-shirts and marching behind a banner indicating they are gay veterans sponsored by MassEquality, according to a copy of the application provided by MassEquality. The group planned to carry signs using the acronym LGBT, referring to lesbian, gay, bisexual, and transgender people. The signs would read, “Another LGBT veteran celebrating St. Patrick’s Day” and “Another LGBT veteran celebrating all veterans” and other, similar slogans.

At Walsh’s urging, parade organizers broke longstanding precedent and invited MassEquality to participate, but with a caveat: Marchers would be barred from wearing T-shirts or holding signs that included the word gay or other references to sexual orientation.

MassEquality rejected the condition because Coredini said the gay community “should never have to silence who they are to be safe, to be equal, or to celebrate other parts of their identities.”

The controversy dates to 1992, when parade organizers refused entry to the Irish-American Gay, Lesbian, and Bisexual Group of Boston. The group won the right to march in state court, but organizers continued to fight.

The case went to the US Supreme Court, which in 1995 handed parade organizers a unanimous victory. The court ruled that although the parade was on public streets, it was a privately organized event protected by the First Amendment right to freedom of speech. The government could not interfere to prevent the Allied War Veterans Council from discriminating against gays and lesbians or any other group.

Mayor Thomas M. Menino refused to march because gays were prohibited from participating openly. Walsh marched in the parade as a state representative as recently as last year. As mayor, he vowed to boycott the event until gay men and women are allowed to march openly. “As of right now, I’m not in the parade,” Walsh said Wednesday.

Earlier this week, parade organizers accused MassEquality of lying on its application by claiming it had 20 gay veterans who wanted to march. At a meeting in the mayor’s office Sunday night, parade organizers said, MassEquality presented one “supposed veteran” and a group of other marchers carrying rainbow flags.

Walsh pushed back Wednesday against the Allied War Veterans Council’s accusation, although he never mentioned the parade organizers by name.

“There are veterans that I’m advocating for that fought for this country to march in the St. Patrick’s Day parade,” Walsh told reporters. “I’m hopeful we can come up with an understanding.”

Despite the breakdown in negotiations, MassEquality said it remained optimistic about the progress achieved this year.

“We know from experience that change comes through conversation and dialogue,” Coredini said. “We were encouraged to have a historic opportunity to meet face-to-face with parade organizers to discuss a contingent involving [gay] veterans, and we did so with open hearts and open minds.”